I fly redeyes on a regular basis, and usually go straight to the office when landing without a problem when I'm in Business.

For me the difference between getting decent sleep and not getting it is the difference between sitting in coach and sitting in business.

Business is quieter and there's way less people moving around you, and they usually have more room to move. The seat is far more comfortable, and I can be getting a few hours of shut eye within minutes of taking off.